1. Technical Field
The present application relates to systems and methods for imaging of an object, particularly systems and methods that involve imaging via tomographic reconstruction of measured frequency samples.
2. Related Art
Tomography is imaging by sections or sectioning. A device used in tomography is called a tomograph, while the image produced is a tomogram. Tomography is used in medicine, archaeology, biology, geophysics, oceanography, materials science, astrophysics and other sciences. The word, tomography, was derived from the Greek word tomos which means “a section,” “a slice,” or “a cutting”. While tomography refers to slice-based imaging, it is also typically applied to three-dimensional (3D) images or four-dimensional images (3D images resolved in time).
In 2006, seminal manuscripts from Candes et al. [Emmanuel J. Candès ET AL., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, 52(2) IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, at 489-509] and Donoho [David Donoho, Compressed sensing, 52(4) IEEE TRANSACTIONS ON INFORMATION THEORY, April 2006, at 1289-1306] created a new field of research labeled “Compressed Sensing” for the reconstruction of images. In general, as stated in the Donoho manuscript, the theory of Compressed Sensing “depends on one specific assumption which is known to hold in many settings of signal and image processing: the principle of transform sparsity.” This has inspired much work that seeks to produce a model that can take advantage of transform sparsity to allow measurement of less data to reconstruct an image, hence speeding up image acquisition. All of these techniques rely on the ability to compress an image itself or some transformation of that image. This body of work is motivated from the seminal manuscript by Donoho where it was stated: “The phenomenon of ubiquitous compressibility raises very natural questions: why go to so much effort to acquire all the data when most of what we get will be thrown away? Can't we just directly measure the part that won't end up being thrown away?” This work has lead to the development of optimization models that are designed to produce transformations that are optimally sparse.